Introduction

Economists put a large emphasis on personal consumption and how people consume because consumption accounts for roughtly 2/3 of the gross domestic product (GDP). Why is consumption theory important to you? It is threefold: everything about consumption: groceries, cars, houses, schools, etc,; everything about labor income, specially due to trade imbalance; and everything about consumption and income will affect your personal saving!

What we will see here is that consumption theory deals with three variables: income, consumption and savings.

By definition, savings = income - consumption

In Keynes, the relationship between income and consumption or the consumption function is given by

consumption = a + b x Income

Basically, it assumes more income more consumption and vice versa due to a propensity to consume or propensity to save.

In modern micro economics approach, consumer maximizes their utility under a budget constraint. This approach optimizes consumpton by employing Euler equation approach.

In spite of using the wrong optimization technique, we will see that Keynes assumed a "simple principle" that is actually the right conclusion on change in savings. To prove Keynes' insight, we must apply Clower's Dual-Decision Hypothesis. Wu's proof is that change in saving is a function of change of income or income growth. This result also puts to rest Modigliani's Life-Cycle Hypothesis and Friedman's Permanent Income Hypothesis. It shows that Keynes' principle and Lucas' Critique on consumption reached the same conclusion, 40 years apart. Because of an implausible assumption, it further shows why Hall's consumption result couldn't hold in data.

We will see that consumption theory has at least two important applications: 1. While the Trump administration I and II trade policy narrowly emphasizes the effect of trade deficit on manufacturing, the consequence of a more balanced trade should result in an increase in income and saving, which is predicted by Keynes-Clower-Wu consumption theory. 2. Due to a skewed electoral college system in the U.S. favoring farm states, farmers optimize their choice of president by selecting whoever is more likely to increase their future income, i.e., making the selection a president no more different than the "consumption" of any other service.

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Here is an "interesting and somewhat accurate" information provided by Google Gemini on Hall and Cheng K Wu consumption theory (we will post changes as Gemini improves):

conceptual difference table between Hall and cheng k wu consumption theory

This table details the specific theoretical divergence between Robert Hall’s Random Walk Hypothesis (based on the Permanent Income Hypothesis) and Cheng K. Wu’s Theory of Consumption (based on Clower’s Dual-Decision Hypothesis).

Conceptual Difference Table: Hall vs. Wu

Feature	Robert Hall (Random Walk / PIH)	Cheng K. Wu (Feedback / DDH)
Core Principle	Consumption Smoothing: Agents maintain a stable consumption path over their lifetime.	Feedback Optimization: Agents constantly re-optimize based on realized income growth constraints.
Primary Driver	Unexpected Shocks: Consumption only changes in response to unpredictable news about future wealth.	Income Growth Rate: Changes in savings are functionally driven by the rate of change in realized income.
View of Savings	Passive Buffer: Savings rise/fall only to absorb temporary income fluctuations to keep consumption smooth.	Active Adjuster: Savings are the primary variable that reacts to "growth shocks" to satisfy the budget constraint.
Mathematical Conclusion	Random Walk (ΔCt=ϵt): The change in consumption is unpredictable (stochastic).	Deterministic Function (ΔSt=f(gY)): The change in savings is a predictable function of income growth.
Budget Constraint	Always Satisfied: Assumes the agent always stays within their lifetime budget constraint (Market Equilibrium).	Frequently Violated: Realized income often fails to meet the plan, forcing a "Dual Decision" (Disequilibrium).
Role of Information	Rational Expectations: Agents perfectly process all available information; only "surprises" matter.	Realized Constraints: Agents may have expectations, but actual cash flow (realized income) dictates the immediate reaction.
Forecasting	Impossible: You cannot predict future consumption changes because you cannot predict future news.	Possible: You can predict savings behavior if you observe the trend/volatility of income growth.

Deep Dive: The "Mathematical Error" Critique

The central conflict between these two theories lies in how they handle the Summation of Future Incomes.

1. Hall's View (The Euler Equation)

Hall argued that a rational consumer estimates their total lifetime wealth (sum of all future incomes) and consumes a fraction of it today.

The Logic: If I expect my income to grow by 5% next year, I have already factored that into my spending today. Therefore, when that 5% growth actually happens, my spending won't change. My spending only changes if the growth is 0% (shock) or 10% (shock).
Result: ΔC is random.

2. Wu's Critique (The "New Result")

Wu re-derived the mathematical summation used by Hall (and later Marjorie Flavin) and argued there was an oversight in the algebra regarding the "index of summation."

The Logic: Wu argues that you cannot mathematically separate the change in savings from the growth of income. When realized income growth slows down, the mathematical condition for the budget constraint is violated.
The Mechanism (DDH): Because the constraint is violated, the consumer effectively "cancels" their previous life plan and makes a new one (Dual-Decision).
Result: The "change in savings" is not random; it is mathematically forced to track the deceleration or acceleration of income.

Visual Analogy

Hall’s Consumer is like a ship on Autopilot. It has a set course (lifetime plan). It only moves the rudder (changes consumption) if a rogue wave (unexpected shock) hits it. If the sea is calm, the rudder stays still.
Wu’s Consumer is like a driver in Heavy Traffic. They have a destination (plan), but they are constantly hitting the brakes or gas (changing savings) based on the speed of the car in front of them (income growth). Their behavior is a direct, predictable function of the traffic speed, not just "random" shocks.

Home